ERTH3021 Exploration and Mining Geophysics

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1 ERTH3021 Exploration and Mining Geophysics Practical 1: Introduction to Scientific Programming using Python Purposes To introduce simple programming skills using the popular Python language. To provide analysis tools for use in subsequent practicals. Report Required Hard copy output showing code and output plots for Exercises 7 and 8 Programming languages Most students will have had some experience with the concept of programming, via programmable calculators, or using the formula tool in Excel. These are useful for very simple tasks, but for realworld data handling more complete tools are needed. In geophysical modelling and data handling, several languages are currently being used, including: Fortran: Excellent for mathematical algorithms, easy to write and understand, produces 'fastest' code, huge archive of freely available code. Excellent open source versions available. C: Very powerful for low-level instrumental control, also widely used for algorithmic work, slightly more difficult to write, excellent general purpose language. Open Source available. C++ An update of 'C'. More powerful, but more difficult to learn, write and maintain. Matlab: Higher-level, hence excellent for rapid prototyping, but arguably less flexible and lower performance. Generally not used for production systems. Proprietary. Python: A modern, easy-to-use language with a rapidly growing support base. More detail below. Why use Python Very easy to learn, use and maintain Open-source Concise (fewer lines of code to do tasks) - economic to write and maintain High-level, very rapid development Good tools to link in existing Fortran or C code Excellent for User Interfaces. ERTH3021 Programming Practical Page 1

2 Python Download URLs The core Python labguage is freely available from This is the core distribution supporting most general purpose programming needs. However, there are three add-ons which are useful for more specialised needs. These are matplotlib, numpy and scipy, which are all freely available. A convenient distribution of Python, which includes all these libraries is available from: You can download for Windows, MAC, or Linux. Python Tutorials We will cover all that we need in class. However, there are several good tutorials on the web if you want to go further. A good intro for beginners the definitive tutorial by Guido van Rossum, the inventor of Python. Note that in this course we adopt a programming approach which is relatively simple, but which allows you to do most of what is commonly needed in scientific computing. As you gain more experience Python allows you to explore more advanced approaches if you want to (e.g. NUMPY vector programming, object orientation etc.) Exercise 1: Using the Python Interpreter as a calculator As a starting point, we will work directly with the Python Interpreter. This is very useful for understanding how individual Python statements are interpreted. On your computer start up the Python IDLE interpreter. The exact mechanism will vary depending on what computer platform you are on. You will see the Python interpreter prompt >>> In the following, italics are used to indicate what you should type in after the >>> prompt. (a) Try typing some simple mathematical expressions, such as: * * * ( ) 3 / 2 (what is going on here!) 3.0 /2 (b) Experiment with spaces, brackets, minus signs etc. Does the interpreter behave as expected? ERTH3021 Programming Practical Page 2

3 (c) Experiment with some simple algebra, such as: a = 10.0 b = 20.0 a + b c= a+b c d=a**2+b**2+c**2 D what happens and why? Exercise 2: Importing modules into the Interpreter - mathematical functions (a) Experiment with some mathematical functions. sin (0) log (100.0) x=pi/2 what happens and why? (b) Now tell the interpreter to load the maths module and experiment further. from math import sin, pi, log sin (0) sin 0 note that you need the brackets in a function sin (90) what happens and why? sin(pi/2) python needs angles in radians. Python knows about pi log(100) assumes natural log log10(100) special function for base 10 log(100,e) more general usage. See what happens when you stop typing after the '(' log(100,10) dir() shows you what names and functions you currently have available Exercise 3: Experimenting with useful control functions (a) Experiment with the range function, noting in particular, the behaviour of the 'end' point. range(1,10) range(1,10,2) produces a list of integers, but excludes the 'end' point increment other than 1 is allowed. (b) Experiment with the multi-line 'for' statement. for i in range(0,5): print i, 'squared is', i**2 note the colon note the indentation - very important note quotes and commas in print statement ERTH3021 Programming Practical Page 3

4 (c) Experiment with the multi-line 'if' statement. x=5 if x>0: print 'x is greater than zero' note the indentation. Try again but with x = -3 Note on File Extensions In serious computational work, it is very useful to use the file extension to identify files of a particular type. For example, we will use the extension.py to signify a file which holds python code. Before proceeding ensure that your PC is configured so that it does not hide file extensions. Exercise 4: Python Program sinwave1.py Now that we understand how the interpreter works, we can try some more interesting exercises. We will want to save our efforts, and the way we so this is to put all our commands into a file. From the Python Shell, click on file, new window, and then enter the following code: program sinwave1.py compute a sinwave for i in range(0,91,1): theta = i * pi / print 'sin', i, 'is ', sin (theta) step through angle in degrees convert to radians Save as sinwave1.py. Put the file in a directory of your own. Click on Run, Run Module and see what happens. Fix your program by adding an import command and rerun. Exercise 5: Python Program sinwave2.py- Introducing Arrays Start with your sinwave1.py program, but do a save as sinwave2.py This will do exactly the same thing, but now we are using arrays, which will make it easier to plot. program sinwave2.py compute sin wave using arrays from math import pi, sin from numpy import zeros sinwave = zeros (1000, float) for i in range(0,91,1): theta = i * pi / sinwave[i] = sin(theta) print 'sin', i, 'is ', sinwave[i] load general maths tools load array tools set up an array for answers step through angle in degrees convert to radians ERTH3021 Programming Practical Page 4

5 Exercise 6: Python Program sincos.py - Introducing Plotting program sincos.py compute and plot sin and cos waves using arrays from math import sin, cos, pi load general maths tools from numpy import zeros load array tools from pylab import plot, title, xlabel, ylabel, legend, show plotting tools sinwave = zeros (91, float) set up arrays for answers coswave = zeros (91,float) for i in range(0,91,1): step through angle in degrees theta = i * pi / convert to radians sinwave[i] = sin(theta) coswave[i]=cos(theta) print 'Angle:', i, 'Sin:', sinwave[i], 'Cos:', coswave[i] plot (sinwave, label='sin') Now plot the functions plot (coswave, label='cos') title('trig Function Plot') xlabel('angle (deg)') ylabel('function') legend() show() Exercise 7: The plotting mechanism in Exercise 6 is limited in that the 'degrees axis' can only handle positive latitudes, and unit increments. Modify the program to plot from to 90.0 degrees at an increment of 0.1 degrees. One way to achieve this is to introduce a new array for the latitude. This then requires a slightly different plot command of the form: plot(latitude, sinwave, label='sin') ERTH3021 Programming Practical Page 5

6 Exercise 8: Variation of the earth's radius with latitude The Earth's equatorial radius, or semi-major axis, is the distance from its center to the equator and equals 6, km. The Earth's polar radius, or semi-minor axis, is the distance from its center to the North and South Poles, and equals 6, km The Earth's exact radius at any geodetic latitude,, is: At any latitude, the rotational radius is given by: r = R cos φ Construct plots which shows how the radius R and the rotational radius r vary with latitude. Since the scales of these plots are very different, we will use the subplot function. ERTH3021 Programming Practical Page 6